Because English is a natural language there are lots of inconsistencies.
The "put" element is indeed the common verb, and that verb is irregular, with the past and past participle the same as the bare infinitive.
The verb "input" is quite old, and in older senses (meaning "impose") it is similar to put. However, prior to computers, the word was quite rare. In the new sense of "put data into a computer" both "he has input some data" and "he has inputted some data" are in use by native speakers, and so both are correct.
You can't justify this based on logic, because language is not logical. If you need a justification, you can say "to input" is derived not as "in + put" but by from the noun "an input", and verbs formed from nouns are all regular.
As noted in the article you link:
In these instances, you should use the past form that comes most naturally to you, while bearing in mind that other people may use a different one.